14949 + Interview Questions in Maths in Class 11 Page 175 InterviewSolution

8701.	The vertices of Delta PQR are P(2,1),Q(-2,3) and R(4,5). Find equation of the median through the vertex R.
Answer» ANSWER :`3x-4y+8=0`

Discussion

8702.	Show that following lines forms an equilateral triangle and find its area 3x^(2)+48xy+23y^(2)=0, 3x-2y+13=0
Answer» ANSWER :`(13)/(SQRT(3))` SQ. units

Discussion

8703.	Find the sum of a geometric series in whicha=16 , r=(1)/(4) ,l = (1)/(64) .
Answer» ANSWER :`21 (21)/(64)`

Discussion

8704.	Verify : sec^(2)theta=1+tan^(2)theta" if "theta=(pi)/(4),
Answer» ANSWER :RIGHT SIDE

Discussion

8705.	A boxis made with square baseand open top .The area of the material used is 192 sq . Cms If the volume of the box is maximum , the dimensions of the box are
Answer» 4,4,8 2,2,4 8,8,4 2,2,2 Answer :C

Discussion

8706.	In the tetrahedron ABCD, A = (1, 2, -3) and G(-3, 4, 5) is the centroid of the tetrahedron. If P is the centroid of the DeltaBCD then AP =
Answer» `(8sqrt(21))/(3)` `(4sqrt(21))/(3)` `4sqrt(21)` `(SQRT(21))/(3)` ANSWER :a

Discussion

8707.	If y = (sin^2x)/(1+cotx)+(cos^2x)/(1+tanx)then dy/dx is equal to
Answer» `COS 2X` `-cos 2x` `2 cos^2x` `cos^3x` ANSWER :B

Discussion

8708.	3x^(2)-2y^(2)=6
Answer» Answer :(i) `2 sqrt(2) " units," 2sqrt(3) "units "` (II) `A(-sqrt(2),0),B (sqrt(2),0)` (iii) `F_(1)(-sqrt(5),0),F_(2)(sqrt(5),0)` `(iv) e=sqrt((5)/(2))` (v) `3sqrt(2)` units

Discussion

8709.	If the point P lies on Z-axis, then coordinates of P are of the form ______ .
Answer» ANSWER :(0, 0, Z)

Discussion

8710.	Find the derivative of the w.r.t.x e ^(2x) log (3x +4)
Answer» ANSWER :`E ^(2X)`

Discussion

8711.	Ifr : Rr_1 = 2: 5 : 12 thenangle A =
Answer» ` 30 ^(@) ` ` 45 ^(@) ` ` 60 ^(@)` ` 90 ^(@) ` ANSWER :D

Discussion

8712.	Let a function f be defined by f (x) =[x-\|x\|]/x for xne 0 and f(0)=2.Then f is :
Answer» comtinuous for all X EXCEPT x=0 continuous everywhere continuos nowhere continuous for all x except x=1 Answer :A

Discussion

8713.	A vertical line passing through (a,4) cuts the curve y^2=4ax at A,B. If the angle subteded by AB at origin istheta, " then" tan theta=
Answer» `pm4/3` `4/3` `-4/3` `pm3/4` ANSWER :B

Discussion

8714.	If bara, barb, barc are the vectors parallel to the coordinate axes in the left handed system then
Answer» `[BARA barb BARC]`=0 `[bara barb barc]ne0` `[barabarb barc]GT0` `[bara barb barc]lt0` Answer :D

Discussion

8715.	If in a triangle ABC sines of angles A and B satisfy the equation 4x^(2) - 2sqrt6 x + 1 =0 then cos(A - B) =
Answer» 0 `1//2` `1//sqrt2` `sqrt3//2` ANSWER :B

Discussion

8716.	Factorise x^2 - 4
Answer» SOLUTION :(X - 2)(x + 2)

Discussion

8717.	Which of the following functions have the graphsymmetrical about the origin?
Answer» f(X) given by `f(x)+f(y)= f((x+y)/(1-xy))` f(x) given by `f(x)+f(y) = f(x sqrt(1-y^(2))+y sqrt(1-x^(2)))` f(x) given by `f(x+y)=f(x) + f(y) AA x, y in R` none of these Answer :A::B::C

Discussion

8718.	Write the negation of "For every real number x,x is less than x +1 . "
Answer» Answer : ''For every''. The NEGATION is There EXISTS a REAL NUMBER X such that x is not less than x + 1.

Discussion

8719.	Find the ratio in which the y-z plane divides the line segment formed by joining points (-2,4,7) and (3,-5,8)
Answer» ANSWER :RATIO is 1:1

Discussion

8720.	(1)/(tan 3x- tanx)-(1)/( cot 3 x- cot x)=
Answer» `SIN2X` `COS2X` `TAN2X` `COT2X` ANSWER :D

Discussion

8721.	If the function f(x)=x^(3)+3(a-7)x^(2)+3(a^(2)-9)x-1has a positive point of maximum , then
Answer» `a in (3,oo)uu(-oo,-3)` `a in(-oo,-3)uu(3,(29)/(7))` `(-oo,7)` `(-oo,(29)/(7))` ANSWER :B

Discussion

8722.	Find the principal solutions of the equation tanx=-(1)/(sqrt(3)).
Answer» ANSWER :`N in Z`

Discussion

8723.	The scalar product of the vector bari+barj+bark " with the unit vector parallel to sum of the vectors " 2bari+4barj-5bark and lambdabari+2barj+3bark is equal to 1. The the value of the constant lambda is
Answer» `1/3` 1 `1/2` 2 Answer :B

Discussion

8724.	Find the 4^thterm in the expansion of (x-2y)^12.
Answer» ANSWER :`1760` `x^9` `Y^3`

Discussion

8725.	Two sample of sizes 50 and 100 given. The mean of these samples respectively are 56 and 50. Then the mean of size 150 combining is
Answer» 55 52 50 None of these ANSWER :B

Discussion

8726.	Convert the following into simplest form (i)Tan ( theta - 14 pi)
Answer» ANSWER :`TAN THETA`

Discussion

8727.	sin20^(@)sin40^(@)sin60^(@)sin80^(@)=?
Answer» `1/16` `3/16` `-3/16` NONE of these Solution :N//A

Discussion

8728.	Find the values of sin67 1^(@)/2,cos67 1^(@)/2,tan67 1^(@)/2,cot67 1^(@)/2
Answer» ANSWER :`SQRT((sqrt2+1)/(2SQRT2)),sqrt((sqrt2-1)/(2sqrt2)), sqrt2+1, sqrt2-1`

Discussion

8729.	2^(Sinx)+2^(Cosx) ge k then k=
Answer» 2 `2^((1)/(2))` `2^(1(1)/(SQRT(2)))` `2^((1)/(sqrt(2)))` ANSWER :C

Discussion

8730.	Assertion (A) : Suppose that alpha- beta is not an odd multipleof (pi)/(2) , m in R-{0,1) and (sin (alpha+beta))/(cos (alpha-beta))=(1-m)/(1+m) then Tan ((pi)/(4)-alpha)=m cot ((pi)/(4)- beta) Reason (R) : for all C,D, & R cos c+cos D= 2 cos ((C+D)/(2)) cos((C-D)/(2)) cos-cosD=-2sin ((C+d)/(2))sin ((C-D)/(2))
Answer» A is TRUE R, is true ` R RARR A` A is true R is true but `R cancel rArr A` A is true, R is false A is false, R is true Answer :A

Discussion

8731.	A rational function is defined as quotient of two polynoials of p(x) and q(x). The domain of the rational function must be all reals except the roots of the equation q(x)=0. The range of rational functions can be found by finding minimum values of the function. In case p(x) and q(x) have a common factor x-beta . Then after cancelling the common factor. The rational functional must assume a value of x=beta which should be delete from the range since beta is not in the domain of the rational function The range of the rational function f(x)=(2x+1)/(2x^(2)+5x+2) must be
Answer» `R-{0}` `R-{-2}` `R-{0, -2}` `R- {0, 2//3}` ANSWER :D

Discussion

8732.	A rational function is defined as quotient of two polynoials of p(x) and q(x). The domain of the rational function must be all reals except the roots of the equation q(x)=0. The range of rational functions can be found by finding minimum values of the function. In case p(x) and q(x) have a common factor x-beta . Then after cancelling the common factor. The rational functional must assume a value of x=beta which should be delete from the range since beta is not in the domain of the rational function The range of the rational function f(x)=(3x+1)/(2x+1) must be
Answer» `R-{- 1/2}` `R-{- 1/3}` `R- { - 3/2}` R Answer :C

Discussion

8733.	A rational function is defined as quotient of two polynoials of p(x) and q(x). The domain of the rational function must be all reals except the roots of the equation q(x)=0. The range of rational functions can be found by finding minimum values of the function. In case p(x) and q(x) have a common factor x-beta . Then after cancelling the common factor. The rational functional must assume a value of x=beta which should be delete from the range since beta is not in the domain of the rational function The range of rational function f(x)=(2x^(2)+5x+2)/(2x+1)
Answer» `R-{0}` `R-{-2}` `R- {0, -2, 2/3}` `R- {3/2}` ANSWER :D

Discussion

8734.	In triangle ABC, line joining the circumcenter and orthocenter is parallel to side AC, then the value of tanA tan C is equal to
Answer» `SQRT(3)` 3 `3sqrt(3)` NONE of these Answer :B

Discussion

8735.	If tan x + tan 2x+tan 3x=tan x tan 2x tan 3x then \|sin 3x+cos 3x\|
Answer» 0 1 `-1` 2 Answer :B

Discussion

8736.	If f: R rarr Rand g:R rarr R are defined by f(x)=x - [x] and g(x)=[x] forx in R, where [x] is the greatest integer not exceeding x , then for every x in R, f(g(x))=
Answer» X 0 `f(x)` `G(x)` Answer :B

Discussion

8737.	Let vecA be vector parallel to line of intersection of planes P _(1) and P _(2) Plane P _(1) is parallel to the vectors 2 hatj + 3 hatk and 4 hatj - 3 hatk and that P _(2) is parallel to hatj - hatk and 3 hatj + 3 hatj, then the angle between vector vecA and a given vector 2 hati + hatj - 2 hatkis
Answer» `pi/2` `pi/4` `pi/6` `(3PI)/(4)` ANSWER :B::D

Discussion

8738.	If A is idempotent matrix A+B=I then B is
Answer» Null MATRIX IDENTITY matrix EQUAL to `B^(2)` equal to `B^(3)` Answer :C

Discussion

8739.	Find the value of cos^(2)37(1^(@))/(2)-sin^(2)37(1^(@))/(2)
Answer» ANSWER :`(SQRT(6)-sqrt(2))/(4)`

Discussion

8740.	f:RtoR,f(x) is differentiablesuch that f(f(x))=k(x^(5)+x),(kne0).Then f(x) is always
Answer» INCREASING decreasing either increasing or decreasing non - monotonic Answer :C

Discussion

8741.	p is the length of the perpendicular drawn from the origin upon a straight line then the locus of mid point of the portion of the line intercepted between the coordinate axes is
Answer» `1/x^2+1/y^2=1/p^2` `1/x^2+1/y^2=2/p^2` `1/x^2+1/y^2=4/p^2` `1/x^2+1/y^2=1/p` ANSWER :B

Discussion

8742.	Assertion (A) : "sin" (pi)/(n)+"sin" (3pi)/(n)+"sin"(5pi)/(n)+....+ to n terms=0 Reason (R): sin alpha+ sin (alpha+ beta)+...+ to n terms =(Sin ((n beta)/(2)))/(Sin beta//2)xxsin ((2 alpha+(n-1)beta)/(2))
Answer» A is TRUE R, is true ` R rArr A` A is true R is true but `R cancel rArr A` A is true, R is FALSE A is false, R is true Answer :A

Discussion

8743.	Evaluate Lim_(xto 2) (x^(5)-32)/(x^(2)-4)
Answer» ANSWER :20

Discussion

8744.	Let f(x)=2sin^(3)x-3sin^(2)x+12sinx+5,0lexlepi//2 .Then f(x) is
Answer» DECREASING in `[0,pi//2]` INCREASING in `[0,pi//2]` increasing in `[0,pi//4]` and decreasing in `[pi//4,pi//2]` increasing in `[0,pi//4]` ANSWER :B

Discussion

8745.	Find the angle which the straight line y=sqrt(3)x-4 makes with the Y-axis.
Answer» ANSWER :`pi//6`

Discussion

8746.	cos h 2x + sin h 2x =
Answer» `(1 + TAN H(x))/(1- tan h(x))` `(1-tan hx)/(1+tan hx)` `(tan h x -1)/(tan h x + 1)` `(1 - tan hx)/(tan h x - 1)` ANSWER :A

Discussion

8747.	Suppose A and B are angles lying in the first quadrant such that tanA=15/8 and tanB =12/5.Find sin A , sin B, cosAand cosB
Answer» SOLUTION :15/17,12/13, 8/17 , 5/13

Discussion

8748.	Evaluate the following limits : Lim_(x to 0) (sin 3x cos 2x)/(sin 2x)
Answer» ANSWER :`3/2`

Discussion

8749.	Prove that the circle x^(2) +y^(2) - 6 x -2 y + 9 = 0 (i) touches the x-axis,(ii) lies entirely inside the circle x^(2) + y^(2) = 18.
Answer» ANSWER :1

Discussion

8750.	If 7 theta = (2n +1) pi,where n = 0 , 1, 2, 3, 4,5, 6 then on the basis of above information, answer the following questions The value of sec pi//7 + sec 3pi//7 +sec 5pi//7 is
Answer» -3 4 `-4` 3 Answer :A

Discussion

Explore topic-wise InterviewSolutions in .

The vertices of Delta PQR are P(2,1),Q(-2,3) and R(4,5). Find equation of the median through the vertex R.

Show that following lines forms an equilateral triangle and find its area 3x^(2)+48xy+23y^(2)=0, 3x-2y+13=0

Find the sum of a geometric series in whicha=16 , r=(1)/(4) ,l = (1)/(64) .

Verify : sec^(2)theta=1+tan^(2)theta" if "theta=(pi)/(4),

A boxis made with square baseand open top .The area of the material used is 192 sq . Cms If the volume of the box is maximum , the dimensions of the box are

In the tetrahedron ABCD, A = (1, 2, -3) and G(-3, 4, 5) is the centroid of the tetrahedron. If P is the centroid of the DeltaBCD then AP =

If y = (sin^2x)/(1+cotx)+(cos^2x)/(1+tanx)then dy/dx is equal to

3x^(2)-2y^(2)=6

If the point P lies on Z-axis, then coordinates of P are of the form ______ .

Find the derivative of the w.r.t.x e ^(2x) log (3x +4)

Ifr : Rr_1 = 2: 5 : 12 thenangle A =

Let a function f be defined by f (x) =[x-|x|]/x for xne 0 and f(0)=2.Then f is :

A vertical line passing through (a,4) cuts the curve y^2=4ax at A,B. If the angle subteded by AB at origin istheta, " then" tan theta=

If bara, barb, barc are the vectors parallel to the coordinate axes in the left handed system then

If in a triangle ABC sines of angles A and B satisfy the equation 4x^(2) - 2sqrt6 x + 1 =0 then cos(A - B) =

Factorise x^2 - 4

Which of the following functions have the graphsymmetrical about the origin?

Write the negation of "For every real number x,x is less than x +1 . "

Find the ratio in which the y-z plane divides the line segment formed by joining points (-2,4,7) and (3,-5,8)

(1)/(tan 3x- tanx)-(1)/( cot 3 x- cot x)=

If the function f(x)=x^(3)+3(a-7)x^(2)+3(a^(2)-9)x-1has a positive point of maximum , then

Find the principal solutions of the equation tanx=-(1)/(sqrt(3)).

The scalar product of the vector bari+barj+bark " with the unit vector parallel to sum of the vectors " 2bari+4barj-5bark and lambdabari+2barj+3bark is equal to 1. The the value of the constant lambda is

Find the 4^thterm in the expansion of (x-2y)^12.

Two sample of sizes 50 and 100 given. The mean of these samples respectively are 56 and 50. Then the mean of size 150 combining is

Convert the following into simplest form (i)Tan ( theta - 14 pi)

sin20^(@)sin40^(@)sin60^(@)sin80^(@)=?

Find the values of sin67 1^(@)/2,cos67 1^(@)/2,tan67 1^(@)/2,cot67 1^(@)/2

2^(Sinx)+2^(Cosx) ge k then k=

In triangle ABC, line joining the circumcenter and orthocenter is parallel to side AC, then the value of tanA tan C is equal to

If tan x + tan 2x+tan 3x=tan x tan 2x tan 3x then |sin 3x+cos 3x|

If f: R rarr Rand g:R rarr R are defined by f(x)=x - [x] and g(x)=[x] forx in R, where [x] is the greatest integer not exceeding x , then for every x in R, f(g(x))=

Let vecA be vector parallel to line of intersection of planes P _(1) and P _(2) Plane P _(1) is parallel to the vectors 2 hatj + 3 hatk and 4 hatj - 3 hatk and that P _(2) is parallel to hatj - hatk and 3 hatj + 3 hatj, then the angle between vector vecA and a given vector 2 hati + hatj - 2 hatkis

If A is idempotent matrix A+B=I then B is

Find the value of cos^(2)37(1^(@))/(2)-sin^(2)37(1^(@))/(2)

f:RtoR,f(x) is differentiablesuch that f(f(x))=k(x^(5)+x),(kne0).Then f(x) is always

p is the length of the perpendicular drawn from the origin upon a straight line then the locus of mid point of the portion of the line intercepted between the coordinate axes is

Assertion (A) : "sin" (pi)/(n)+"sin" (3pi)/(n)+"sin"(5pi)/(n)+....+ to n terms=0 Reason (R): sin alpha+ sin (alpha+ beta)+...+ to n terms =(Sin ((n beta)/(2)))/(Sin beta//2)xxsin ((2 alpha+(n-1)beta)/(2))

Evaluate Lim_(xto 2) (x^(5)-32)/(x^(2)-4)

Let f(x)=2sin^(3)x-3sin^(2)x+12sinx+5,0lexlepi//2 .Then f(x) is

Find the angle which the straight line y=sqrt(3)x-4 makes with the Y-axis.

cos h 2x + sin h 2x =

Suppose A and B are angles lying in the first quadrant such that tanA=15/8 and tanB =12/5.Find sin A , sin B, cosAand cosB

Evaluate the following limits : Lim_(x to 0) (sin 3x cos 2x)/(sin 2x)

Prove that the circle x^(2) +y^(2) - 6 x -2 y + 9 = 0 (i) touches the x-axis,(ii) lies entirely inside the circle x^(2) + y^(2) = 18.

If 7 theta = (2n +1) pi,where n = 0 , 1, 2, 3, 4,5, 6 then on the basis of above information, answer the following questions The value of sec pi//7 + sec 3pi//7 +sec 5pi//7 is